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PhD Public Lecture (Math) - Brandon Doherty

Friday, July 30, 2021
2:00 pm
Virtual via Zoom

"Cubical models of higher categories"

Models of higher categories based on simplicial and cubical sets have played a key role in the development of categorical homotopy theory. In this talk we describe a new model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We discuss the proof that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor, and a new theory of cones in cubical sets which is used in this proof. We also introduce the homotopy category and mapping spaces of a fibrant cubical set, and characterize weak equivalences between fibrant cubical sets in terms of these concepts.

Adriana Dimova

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